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This paper considers the problem of phase recovery of QPSK signals with phase-locked loops (PLL) using two new phase error detectors (PEDs) which are designed to minimize the probability of making a symbol decision error. The new PEDs resemble the PED derived from the maximum likelihood criterion. However, the new PEDs penalize matched filter outputs that are close to decision region boundaries. This penalty gives rise to faster converging PLLs relative to PLLs using the maximum likelihood PED, as shown in simulation results. The S-curves for the PEDs are used as a tool to gain insight into the behavior of the new PEDs.